What doubts does Winnie have about the Tucks's story?

The Tucks tell Winnie that 87 years ago they arrived at the woods with the idea of building a farm and settling down. On their first night, just before they set up camp, they saw a spring and, being thirsty, they all drank from it. The father even carved a T in a nearby tree to mark the spot.
Not long after, they each survived a series of bad accidents unscathed. Jessie, for example, was unharmed when he fell head first from a tree. Ten years later, they realized that none of them had aged. The water from the spring had made them immortal.
In the the following chapter, the author states that, Winnie sees herself as a realist:

Winnie did not believe in fairytales. She had never longed for a magic wand, did not expect to marry a prince, and was scornful . . . of her grandmother's elves.

Yet she listens to the Tuck story open-mouthed, not knowing exactly what to think. One part of her thinks the story is too extraordinary to be true, and the other thinks that the Tucks are too genuinely excited about it for it to be a lie. In the end, she happily goes home with them.